The decision by the government to give headteachers the power to sack BNP members is welcome news to black and Asian parents throughout the country. It's a sign that the government does listen to reason, not least from the black middle classes.

It is no big secret that state education has a racial problem. The excessive numbers of black pupils excluded suggests as much. The fact that only one person of African-Caribbean background secured a place at Oxford University last year indicates that the issues continue into higher education. With this in mind, who can blame a black parent for being horrified at the prospect of their child being tutored by a member of the racist British National Party? How can we trust them to teach "without prejudice".

The BNP activist Adam Walker, while working as a technology teacher, described immigrants as "savage animals" and "filth" and claimed that parts of Britain are a "dumping ground for the … third world". That is not surprising. That is what most BNP members think of black people and our contribution to Britain. It's not the kind of opinion that gives a black parent confidence in the teaching profession. Instead it leaves parents like me wondering how many more BNP teachers are out there.

That was the question I put to David Cameron at his "conversation with the community" hustings in Peckham, south London a few weeks before the general election this year. He didn't answer whether he would or wouldn't deliver his children daily into the care of such a person. But he did acknowledge that being a teacher and being a member of the BNP were incompatible. And to the cheers of the well-heeled buppies (black middle classes) in attendance he promised there and then that should he get into power he would change the law if necessary to give headteachers the power to sack staff who were members of the BNP.

It's five months since the election and I have waited for the moment when the prime minister would fulfil that promise. I lived in hope. But with so many other pressing matters on the coalition agenda, I didn't think the concerns of parents like me were that high on the government's priorities.

In those five months, I have withdrawn my older daughter from the school she attended out of concern about the attitude of one or two of the teachers. Call it paranoia if you want to, but unless teachers have the same sort of police checks on their prejudice as they do on their criminal conduct, black parents can never be entirely sure if the racism they encounter in the workplace is reflected in their children's school life.

One cannot legislate for casual prejudice, I realise that. But I would be more reassured about the motives of the teachers if I knew that they were not members of a racist party.

This is what the Tory London Assembly member James Cleverly fails to understand when he defends the right of teachers to be BNP members. As a black parent he ought to know that it is not the political affiliation but the racism that comes with it that threatens the safety and wellbeing, not to talk of the education, of his children.

Until Tuesday I didn't really believe that someone like me could influence government policy. It is exhilarating to know that David Cameron has not left me out of his "big society".